Coherent control experiments atoms

Periodic spectral phase-modulation functions have been used in numerous experiments and theoretical studies on coherent control of atoms [75-79] and molecules [24, 25, 42, 68, 73, 80-85]. Applying a sinusoidal phase-modulation function of the form... 

The previous sections focused on the case of isolated atoms or molecules, where coherence is fully maintained on relevant time scales, corresponding to molecular beam experiments. Here we proceed to extend the discussion to dense environments, where both population decay and pure dephasing [77] arise from interaction of a subsystem with a dissipative environment. Our interest is in the information content of the channel phase. It is relevant to note, however, that whereas the controllability of isolated molecules is both remarkable [24, 25, 27] and well understood [26], much less is known about the controllability of systems where dissipation is significant [78]. Although this question is not the thrust of the present chapter, this section bears implications to the problem of coherent control in the presence of dissipation, inasmuch as the channel phase serves as a sensitive measure of the extent of decoherence. 

Although coherent control is now a mature field, much remains to be accomplished in the study of the channel phase. There is no doubt that coherence plays an important role in large polyatomic molecules as well as in dissipative systems. To date, however, most of the published research on the channel phase has focused on isolated atoms and diatomic molecules, with very few studies addressing the problems of polyatomic and solvated molecules. The work to date on polyatomic molecules has been entirely experimental, whereas the research on solvated molecules has been entirely theoretical. It is important to extend the experimental methods from the gas to the condensed phase and hence explore the theoretical predictions of Section VC. Likewise interesting would be theoretical and numerical investigations of isolated large polyatomics. A challenge to future research would be to make quantitative comparison of experimental and numerical results for the channel phase. This would require that we address a sufficiently simple system, where both the experiment and the numerical calculation could be carried out accurately. 

There are a number of excellent reviews on atoms in intense laser fields [9]. Consequently, we will focus our attention on the experimental aspects of the behaviour of simple molecules in such fields. Most of the work to date has used a laser field of a single frequency, but experiments are presently underway where manipulation of dissociation pathways is being attempted by varying the phase between the fundamental and the second harmonic [10]. This simplest example of coherent control of chemical reactions will be touched on briefly at the end of the paper. 

The possibility to use laser radiations to achieve the so-called "coherent control" of molecular dissociation or of atomic photoionization has been predicted since the advent of laser sources in the early sixties. It was expected that, thanks to the coherence and monochromaticity properties of the laser light, one could selectively choose a dissociation channel and the spatial orientation of ejection of the fragments (either ions or electrons or even neutrals) in an elementary chemical process. However, earlier attempts, based on simple photoabsorption processes, have been unsuccessful and it is only recentiy that experiments have been shown to enable one to achieve such a goal in some selected systems. Amongst the various scenarios which have been explored, one of the most promising is based on the realization of quantum interferences in so-called "two-colour" photodissociation or... 

The formation of a bound moleeule out of two colliding ultracold atoms is a simple example of a laser-induced ehemieal reaction at very low temperature. At room or even higher temperatures, as discussed in Chapter 8 by Evgueny Shapiro and Moshe Shapiro, the well-established field of coherent control relies upon the possibility of shaping laser pulses to eontrol the output of chemical reactions. Whether similar schemes ean be applied to the PA and stabilization reactions at low temperatures has been an open question. To give an answer, one should carefully explore the feasibility and the effieiency of pump-dump experiments to selectively create ultracold molecules in the w = 0 level of their ground elecfionic state. 

We should remark that, in order to observe genuine spontaneous effects in these single atom cavity experiments it is important to control the blackbody field and to reduce the number of thermal photons in the mode well below unity (k3X/h uigf < I), which requires very low temperatures. If this condition is not fulfilled, one observes the oscillations of the atomic system in the random thermal field, which also present interesting features. A discussion of these effects, along with the effect of quantum collapse and revivals of Rabi nutation in an applied coherent field can be found in re-... 

Here we extend the simple three-level EIT system to mote complicated and versatile configurations in a multi-level atomic system coupled by multiple laser fields. We show that with multiple excitation paths provided by different laser fields, phase-dependent quantum interference is induced either constractive or destractive interfereiKe can be realized by varying the relative phases among the laser fields. Two specific examples are discussed. One is a three-level system coupled by bichromatic coupling and probe fields, in which the phase dependent interference between the resonant two-photon Raman transitions can be initiated and controlled. Another is a four-level system coupled by two coupling fields and two probe fields, in which a double-EIT confignration is created by the phase-dependent interference between three-photon and one-photon excitation processes. We analyze the coherently coupled multi-level atomic system and discuss the control parameters for the onset of constructive or destructive quantum interference. We describe two experiments performed with cold Rb atoms that can be approximately treated as the coherently coupled three-level and four-level atomic systems respectively. The experimental results show the phase-dependent quantum coherence and interference in the multi-level Rb atomic system, and agree with the theoretical calculations based on the coherently coupled three-level or four-level model system. 

Phase-dependent coherence and interference can be induced in a multi-level atomic system coupled by multiple laser fields. Two simple examples are presented here, a three-level A-type system coupled by four laser fields and a four-level double A-type system coupled also by four laser fields. The four laser fields induce the coherent nonlinear optical processes and open multiple transitions channels. The quantum interference among the multiple channels depends on the relative phase difference of the laser fields. Simple experiments show that constructive or destructive interference associated with multiple two-photon Raman channels in the two coherently coupled systems can be controlled by the relative phase of the laser fields. Rich spectral features exhibiting multiple transparency windows and absorption peaks are observed. The multicolor EIT-type system may be useful for a variety of application in coherent nonlinear optics and quantum optics such as manipulation of group velocities of multicolor, multiple light pulses, for optical switching at ultra-low light intensities, for precision spectroscopic measurements, and for phase control of the quantum state manipulation and quantum memory. 

One more trend in laser control is based on the use of the property of coherence of the laser light. To effect coherent laser control, it is necessary that not only the light, but also the atom (or molecule) should be in a coherent state during the interaction. For atoms in a beam or in a low-pressure gas, the phase relaxation time of their wave functions depends on spontaneous decay or on collisions and can be comparatively long (from 10 to 10 s). It was for precisely this reason that the main experiments on coherent interaction were conducted with atoms. These experiments led in the final analysis to the discovery of new effects, such as coherent population trapping (Arimondo 1996), electromagnetically induced transparency (Harris 1997), and the slow-light effect (Hau et al. 1999 Kash et al. 1999). 

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